SOLUTION: A can do a piece of work in 80 days and B in 64 days and C in 160 days. All begin to do it altogether but A leaves after 20 days and B leaves after 15 days before completion of the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do a piece of work in 80 days and B in 64 days and C in 160 days. All begin to do it altogether but A leaves after 20 days and B leaves after 15 days before completion of the      Log On


   

Question 847000: A can do a piece of work in 80 days and B in 64 days and C in 160 days. All begin to do it altogether but A leaves after 20 days and B leaves after 15 days before completion of the work. How long did the work last??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction of the work does A
get done in 20 days?
+20%2A%281%2F80%29+=+1%2F4+
What fraction does B get done in
15 days?
+15%2A%28+1%2F64+%29+=+15%2F64+
The fraction of the work that is left is:
+1+-+1%2F4+-+15%2F64+
+1+-+16%2F64+-+15%2F64+
+1+-+31%2F64+=+33%2F64+
C has to do this fraction of the work in
the remaining days, +d+
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C's rate of working is ( i job ) / ( 160 days )
+1%2F160+
I can say:
+%28+33%2F64+%29+%2F+d+=+1%2F160+
+33+%2F+%28+64d+%29+=+1%2F160+
+33%2F%28+2d+%29+=+1%2F5+
+5%2A33+=+2d+
+d+=+165%2F2+
+d+=+82.5+
The work lasts 82.5 days
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Check my math, and you might want
a 2nd opinion on this , too